Off-center rattling modes and glasslike thermal conductivity in the type-I clathrate ${\text{Ba}}_8{\text{Ga}}_{16}{\text{Sn}}_{30}$

Type-I clathrate ${\text{Ba}}_8{\text{Ga}}_{16}{\text{Sn}}_{30}$ is unique for showing glasslike behavior in the lattice thermal conductivity ${\kappa }_{\text{L}}$ irrespective of the charge carrier type. For better understanding the relation between this behavior and guest rattling, polarized Raman-scattering measurements have been performed on carrier-tuned single crystals. The appearance of a symmetry-forbidden mode in the $E_g$ symmetry spectrum indicates that the Ba atoms are rotating among the off-center positions in the tetrakaidecahedron. On cooling from 300 to 4 K, the energies of $E_g$ and $T_{2g}$ guest modes decrease by 15% and 25%, respectively. This drastic decrease originates from the strongly anharmonic potential with a quartic term of the atomic displacement. The energy of $14{\text{cm}}^{-1}$ for the $T_{2g}$ mode at 4 K is the lowest among intermetallic clathrates. These results for ${\text{Ba}}_8{\text{Ga}}_{16}{\text{Sn}}_{30}$ are compared with those for type-I ${\text{Eu}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$ and ${\text{Sr}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$ whose ${\kappa }_{\text{L}}\left(T\right)$ show similar glasslike behavior with a plateau. The comparison between three systems indicates that the guest rattling energy is proportional to the temperature range of the plateau in ${\kappa }_{\text{L}}\left(T\right)$.

Figure 1

Temperature dependence of lattice thermal conductivity ${\kappa }_{\text{L}}$ for $n$- and $p$-type $\beta {\text{-Ba}}_8{\text{Ga}}_{16}{\text{Sn}}_{30}$, $\beta {\text{-Eu}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$ [open circles; our data, open squares; Bentien et al. (Ref. 5)], and ${\text{Sr}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$ (Ref. 8). The arrows show the temperature ranges of the plateaus.

Figure 2

(a) The dodecahedral and tetrakaidecahedral cages of the type-I clathrate structure. The center of the former is a $2a$ (Ba1) site and that of the latter is a $6d$ (Ba2) site. (b) On-center vibrational modes of Ba2 with one $E_g$ mode and doubly degenerate $T_{2g}$ modes. (c) Off-center rotational modes of Ba2 with $E_g$, $T_{2g}$, and $A_{1g}$ modes. The modes marked by (A) are additional modes which are allowed only for off-center vibrations.

Figure 3

Raman-scattering spectra of $E_g$ and $T_{2g}$ modes for $n$- and $p$-type $\beta {\text{-Ba}}_8{\text{Ga}}_{16}{\text{Sn}}_{30}$ at 4 K. The spectra at 2 K for $\beta {\text{-Eu}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$ and ${\text{Sr}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$ with $n$-type carriers are taken from Ref. 15. The peaks marked by (A) and (1) are the guest modes, and other peaks (2)–(9) are the cage modes (see text).

Figure 4

Raman-scattering spectra of $E_g$ and $T_{2g}$ modes for $n$-type $\beta {\text{-Ba}}_8{\text{Ga}}_{16}{\text{Sn}}_{30}$ at various temperatures from 4 to 300 K. The spectra at 300 K are reproducible before (1st) and after cooling (2nd).

Figure 5

Temperature dependence of vibrational energy of the cage modes $E_g$ (squares) and $T_{2g}$ (circles) for $n$-type $\beta {\text{-Ba}}_8{\text{Ga}}_{16}{\text{Sn}}_{30}$. The closed squares represent $E_g\left(5\right)$ (see text).

Figure 6

Temperature dependence of rattling energy of the guest modes $E_g\left(\text{A}\right)$ and $T_{2g}\left(1\right)$ for (a) $n$-type $\beta {\text{-Ba}}_8{\text{Ga}}_{16}{\text{Sn}}_{30}$, $\beta {\text{-Eu}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$, and ${\text{Sr}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$ (Refs. 15, 16), and for (b) $n$- and $p$-type $\beta {\text{-Ba}}_8{\text{Ga}}_{16}{\text{Sn}}_{30}$.

Figure 7

Temperature range of the plateau in the lattice thermal conductivity ${\kappa }_{\text{L}}\left(T\right)$ versus rattling energy of $\beta {\text{-Ba}}_8{\text{Ga}}_{16}{\text{Sn}}_{30}$, $\beta {\text{-Eu}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$, and ${\text{Sr}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$. The vertical bars give the temperature range of the plateau shown in Fig. 1 and the horizontal bars are the ranges of rattling energy determined by the Raman-scattering measurements.